QUANTUM KIRWAN MORPHISM AND GROMOV–WITTEN INVARIANTS OF QUOTIENTS III

This is the third in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology QH_G(X) of a smooth polarized complex projective variety X with the action of a connected complex reductive group G to the orbifold quantum cohomology QH(X//G) of its geometric invariant theory quotient X//G, and prove that it intertwines the genus zero gauged Gromov–Witten potential of X with the genus zero Gromov–Witten graph potential of X//G. We also give a formula for a solution to the quantum differential equation on X//G in terms of a localized gauged potential for X. These results overlap with those of Givental [14], Lian–Liu–Yau [21], Iritani [20], Coates–Corti–Iritani–Tseng [11], and Ciocan–Fontanine–Kim [7], [8].